On character tables of wreath products

Mattarei, Sandro (1995) On character tables of wreath products. Journal of Algebra, 175 (1). pp. 157-178. ISSN 0021-8693

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Abstract

The theory of characters of wreath products of finite groups is very well known. The basic fact is that any invariant irreducible character of the base group is extendible to the wreath product, and an extension can be computed explicitly. In this paper we shall study the character table of a wreath product as a whole, rather than single characters. We shall prove that the character table of a wreath product G ≀ A is determined uniquely by the permutation group A and the character table of G. This result provides a powerful tool for increasing the derived length of a group, while keeping its character table under control. We shall employ it in Section 4 to construct pairs (G, H) of groups with identical character tables and derived lengths n and n + 1, for any given natural number n ≥ 2.

Keywords:Wreath products, Finite groups
Subjects:G Mathematical and Computer Sciences > G100 Mathematics
Divisions:College of Science > School of Mathematics and Physics
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ID Code:18522
Deposited On:16 Nov 2016 13:33

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